ecuació de estat: sólid ideal

a_{V}P+a_{P}V = kT

P = (1/a_{V})·( kT+(-1)·a_{P}V )

V = (1/a_{P})·( kT+(-1)·a_{V}P )

T = (1/k)·( a_{V}P+a_{P}V )

d_{V}[P] = (-1)·( a_{P}/a_{V} )

d_{P}[V] = (-1)·( a_{V}/a_{P} )

d_{T}[P] = ( k/a_{V} )

d_{T}[V] = ( k/a_{P} )

d_{V}[T] = ( a_{P}/k )

d_{P}[T] = ( a_{V}/k )

ecuacions de estat

PV = kT·sin(aT)

P = (1/V)·kT·sin(aT)

V = (1/P)·kT·sin(aT)

T = (1/a)·sin-pow[1]( (PV)/k )

d_{V}[P] = (-1)·(P/V)

d_{P}[V] = (-1)·(V/P)

d_{T}[P] = (P/T)+(P·a)·( ( 1/( sin(aT) )^{2} )+(-1) )^{(1/2)}

d_{T}[V] = (V/T)+(V·a)·( ( 1/( sin(aT) )^{2} )+(-1) )^{(1/2)}

d_{P}[T] = (1/a)·(1/P)·( 1/( (1/(aT))+( ( 1/( sin(aT) )^{2} )+(-1) )^{(1/2)} ) )

d_{V}[T] = (1/a)·(1/V)·( 1/( (1/(aT))+( ( 1/( sin(aT) )^{2} )+(-1) )^{(1/2)} ) )

PV = kT·cos(aT)

P = (1/V)·kT·cos(aT)

V = (1/P)·kT·cos(aT)

T = (1/a)·cos-pow[1]( (PV)/k )

d_{V}[P] = (-1)·(P/V)

d_{P}[V] = (-1)·(V/P)

d_{T}[P] = (P/T)+(-1)·(P·a)·( ( 1/( cos(aT) )^{2} )+(-1) )^{(1/2)}

d_{T}[V] = (V/T)+(-1)·(V·a)·( ( 1/( cos(aT) )^{2} )+(-1) )^{(1/2)}

d_{P}[T] = (1/a)·(1/P)·( 1/( (1/(aT))+(-1)·( ( 1/( cos(aT) )^{2} )+(-1) )^{(1/2)} ) )

d_{V}[T] = (1/a)·(1/V)·( 1/( (1/(aT))+(-1)·( ( 1/( cos(aT) )^{2} )+(-1) )^{(1/2)} ) )

ecuació de estat

PV = kT·e^{aT}

V = (1/P)·kT·e^{aT}

P = (1/V)·kT·e^{aT}

T = (1/a)·e-pow[1]( (PV)/k )

d_{P}[V] = (-1)·(V/P)

d_{V}[P] = (-1)·(P/V)

d_{T}[V] = (V/T)+(V·a)

d_{T}[P] = (P/T)+(P·a)

d_{V}[T] = (P/k)·(1/a)·( 1/(1+(aT)) )·( k/(PV) )·(aT)

d_{P}[T] = (V/k)·(1/a)·( 1/(1+(aT)) )·( k/(PV) )·(aT)

PV = kT·ln(aT)

V = (1/P)·kT·ln(aT)

P = (1/V)·kT·ln(aT)

T = (1/a)·ln-pow[1]( (PV)/k )

d_{P}[V] = (-1)·(V/P)

d_{V}[P] = (-1)·(P/V)

d_{T}[V] = (V/T)+(k/P)

d_{T}[P] = (P/T)+(k/V)

d_{V}[T] = (P/k)·(1/a)·( 1/(1+( 1/ln(aT) )) )·( k/(PV) )·(aT)

d_{P}[T] = (V/k)·(1/a)·( 1/(1+( 1/ln(aT) )) )·( k/(PV) )·(aT)

ecuacions de estat

P·V = kT

q·V = kT

(P·V)^{2}+E[a]·(P·V) = (kT)^{2}

(q·V)^{2}+E[b]·(q·V) = (kT)^{2}

(P·V)^{2}+E[c]·(kT) = (kT)^{2}

(q·V)^{2}+E[d]·(kT) = (kT)^{2}

T = (1/k)·( (PV)^{2}+E[a](PV) )^{(1/2)}

d_{V}[ T ] = (1/2)·(1/k)·( 1/(kT) )·( P^{2}·(2V)+(E[a]·P) )

d_{P}[ T ] = (1/2)·(1/k)·( 1/(kT) )·( V^{2}·(2P)+(E[a]·V) )

V = (1/2)·(1/P^{2})·( (-1)·E[a]P+( (E[a]P)^{2}+(-4)·P^{2}·(kT)^{2} )^{(1/2)} )

P = (1/2)·(1/V^{2})·( (-1)·E[a]V+( (E[a]V)^{2}+(-4)·V^{2}·(kT)^{2} )^{(1/2)} )

d_{T}[V] = (-1)·(1/P^{2})·( 1/(V+( E[a]/(2P) )) )·k^{2}·T

d_{T}[P] = (-1)·(1/V^{2})·( 1/(P+( E[a]/(2V) )) )·k^{2}·T

d_{P}[V] = ...

... (-2)·(V/P)+(-1)·(E[a]/P^{2})+(1/2)·(1/P^{3})·( 1/(V+( E[a]/(2P) )) )·( E[a]^{2}+(-4)·(kT)^{2} )

d_{V}[P] = ...

... (-2)·(P/V)+(-1)·(E[a]/V^{2})+(1/2)·(1/V^{3})·( 1/(P+( E[a]/(2V) )) )·( E[a]^{2}+(-4)·(kT)^{2} )

d_{T}[ E[a] ] = ( (2k^{2})/(P·V) )·T

d_{T}[ E[b] ] = ( (2k^{2})/(q·V) )·T

d_{T}[ E[c] ] = k+( (P·V)^{2}/(T^{2}) )

d_{T}[ E[d] ] = k+( (q·V)^{2}/T^{2} )

d_{V}[ E[a] ] = (-1)·(1/P)·( (kT)/V )^{2}+(-P)

d_{P}[ E[a] ] = (-1)·(1/V)·( (kT)/P )^{2}+(-V)

d_{V}[ E[c] ] = (-1)·P^{2}·( V/(kT) )

d_{P}[ E[c] ] = (-1)·V^{2}·( P/(kT) )

V = (1/P)·( (kT)^{2}+(-1)·E[c](kT) )^{(1/2)}

P = (1/V)·( (kT)^{2}+(-1)·E[c](kT) )^{(1/2)}

d_{T}[ V ] = (1/2)·(1/P)·( 1/(PV) )·( k^{2}·(2T)+(-1)·E[c]·k )

d_{T}[ P ] = (1/2)·(1/P)·( 1/(PV) )·( k^{2}·(2T)+(-1)·E[c]·k )

d_{P}[ V ] = (-1)·(V/P)

d_{V}[ P ] = (-1)·(P/V)

T = (1/2)·(1/k^{2})·( E[c]k+( (E[c]k)^{2}+(-4)·k^{2}·(PV)^{2} )^{(1/2)} )

d_{P}[ T ] = (-1)·( 1/k^{2} )·( ( 1/(T+(-1)·( E[c]/(2k) )) )·( V^{2}·P )

d_{V}[ T ] = (-1)·( 1/k^{2} )·( ( 1/(T+(-1)·( E[c]/(2k) )) )·( P^{2}·V )

discus de vinil

Agulla
R·d_{t}[q(t)]


Tema musical
(q/x)


R·d_{t}[q(t)] = d_{t}[T(t)] + R_{0}·(q_{0}/x)·d_{t}[x]

circuit térmic

estufa de llum y congelador de llum:
(-1)·d_{t}[T(x)T(t)] + (a/R)·(T(x)T(t)) = V(x,t)
(B/R)·d_{xx}^{2}[T(x)T(t)] + (a/R)·(T(x)T(t)) = V(x,t)
T(x)T(t) = e^{(R/B)^{(1/2)}xi}e^{(-t)}+(R/a)·( k+nx ) <==> V(x,t) = k+nx


calefactor y aire acondicionat:
(-1)·d_{t}[T(x)T(t)] + (-1)·(a/R)·(T(x)T(t)) = V(x,t)
(B/R)·d_{xx}^{2}[T(x)T(t)] + (-1)·(a/R)·(T(x)T(t)) = V(x,t)
T(x)T(t) = e^{(-1)·(R/B)^{(1/2)}x}e^{t}+(-1)·(R/a)·( k+nx ) <==> V(x,t) = k+nx


ecuació del calor:


(B/R)·d_{xx}^{2}[T(x)T(t)] + d_{t}[T(x)T(t)] = 0


radiador y nevera:
(-1)·d_{t}[T(x)T(t)] = V(x,t)
(B/R)·d_{xx}^{2}[T(x)T(t)] = V(x,t)
T(x)T(t) = e^{(R/B)^{(1/2)}x}e^{(-t)} <==> V(x,t) = e^{x}e^{(-t)}
T(x)T(t) = e^{(R/B)^{(1/2)}x}e^{(-t)}+k·( (-t)+(1/2)·x^{2} ) <==> V(x,t) = e^{x}e^{(-t)}+k

calor eléctric

T(t) = R·q(t)


m·∫ d_{T}[Q(T)] d[T] = q(t)·V(t)
m·∫ d_{T}[Q(T)] d_{t}[T(t)] d[t] = q(t)·V(t)
m·d_{T}[Q(T)]·R = V(t)


calor especifico = intensidad del corriente


m·d_{T}[Q(T)] = d_{t}[q(t)]

índex de física

índex de etiquetes de física

termodinàmica de gas ideal cúbico positivo-positivo

(PV)^{3} + (kT)·(PV)^{2} + (kT)^{2}(PV) = (kT)^{3}

a^{3}+(-1)·a^{2}+(-1)·a+(-1) = 0
b^{3}+b^{2}+b+(-1) = 0


a = ( x+(1/3) )
b = ( y+(-1)·(1/3) )


( x^{3}+(1/3)·x+(1/27) )+(-1)·( (2/3)·x+(1/9) )+(-1)·( x+(1/3) )+(-1) = 0
( y^{3}+(1/3)·y+(-1)(1/27) )+( (-1)·(2/3)·y+(1/9) )+( y+(-1)(1/3) )+(-1) = 0


( x^{3}+(-1)·(4/3)·x+( (1/27)+(-1)·(1/9)+(-1)·(1/3) )+(-1) = 0
( y^{3}+(2/3)·y+( (-1)(1/27)+(1/9)+(-1)·(1/3) )+(-1) = 0


( x^{3}+(-1)·(4/3)·x+(-1)·(38/27) = 0
( y^{3}+(2/3)·y+(-1)·(34/27) = 0


T(P,V) = a·( 1/k )·PV


P(T,V) = b·k·( T/V )
V(T,P) = b·k·( T/P )


d_{P}[ T(P,V) ] = a·( 1/k )·V
d_{V}[ T(P,V) ] = a·( 1/k )·P


d_{T}[ P(T,V) ] = b·k·(1/V)
d_{V}[ P(T,V) ] = (-1)·b·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = b·k·(1/P)
d_{P}[ V(T,P) ] = (-1)·b·k·( 1/P^{2} )

termodinàmica del gas cuadrático negativo

(PV)^{2} + (-1)·(kT)·(PV) = (kT)^{2}


T(P,V) = ( ((-1)+5^{(1/2)})/2 )·( 1/k )·PV


P(T,V) = ( (1+5^{(1/2)})/2 )·k·( T/V )
V(T,P) = ( (1+5^{(1/2)})/2 )·k·( T/P )


d_{P}[ T(P,V) ] = ( ((-1)+5^{(1/2)})/2 )·( 1/k )·V
d_{V}[ T(P,V) ] = ( ((-1)+5^{(1/2)})/2 )·( 1/k )·P


d_{T}[ P(T,V) ] = ( (1+5^{(1/2)})/2 )·k·(1/V)
d_{V}[ P(T,V) ] = (-1)·( (1+5^{(1/2)})/2 )·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = ( (1+5^{(1/2)})/2 )·k·(1/P)
d_{P}[ V(T,P) ] = (-1)·( (1+5^{(1/2)})/2 )·k·( 1/P^{2} )

termodinàmica de gas ideal cuadrático positivo

(PV)^{2} + (kT)·(PV) = (kT)^{2}


T(P,V) = ( 1/(2k^{2}) )( kPV+( (kPV)^{2}+4(kPV)^{2} )^{(1/2)} )
T(P,V) = ( 1/(2k^{2}) )( kPV+5^{(1/2)}·kPV )
T(P,V) = ( 1/(2k^{2}) )( (1+5^{(1/2)})·kPV )


T(P,V) = ( (1+5^{(1/2)})/2 )·( 1/k )·PV


P(T,V) = ( 1/(2V^{2}) )( (-1)·kTV+( (kTV)^{2}+4(kTV)^{2} )^{(1/2)} )
P(T,V) = ( 1/(2V^{2}) )( (-1)·kTV+5^{(1/2)}·kTV )
P(T,V) = ( 1/(2V^{2}) )( ((-1)+5^{(1/2)})·kTV )


V(T,V) = ( 1/(2P^{2}) )( (-1)·kTP+( (kTP)^{2}+4(kTP)^{2} )^{(1/2)} )
V(T,V) = ( 1/(2P^{2}) )( (-1)·kTP+5^{(1/2)}·kTP )
V(T,V) = ( 1/(2P^{2}) )( ((-1)+5^{(1/2)})·kTP )


P(T,V) = ( ((-1)+5^{(1/2)})/2 )·k·( T/V )
V(T,P) = ( ((-1)+5^{(1/2)})/2 )·k·( T/P )


d_{P}[ T(P,V) ] = ( (1+5^{(1/2)})/2 )·( 1/k )·V
d_{V}[ T(P,V) ] = ( (1+5^{(1/2)})/2 )·( 1/k )·P


d_{T}[ P(T,V) ] = ( ((-1)+5^{(1/2)})/2 )·k·(1/V)
d_{V}[ P(T,V) ] = (-1)·( ((-1)+5^{(1/2)})/2 )·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = ( ((-1)+5^{(1/2)})/2 )·k·(1/P)
d_{P}[ V(T,P) ] = (-1)·( ((-1)+5^{(1/2)})/2 )·k·( 1/P^{2} )

termodinàmica de gas ideal

PV = kT


T(P,V) =  (1/k)·PV


P(T,V) =  k·( T/V )
V(T,P) =  k·( T/P )


d_{P}[ T(P,V) ] = (1/k)·V
d_{V}[ T(P,V) ] = (1/k)·P


d_{T}[ P(T,V) ] = k·(1/V)
d_{V}[ P(T,V) ] = (-1)·k·( 1/V^{2} )


d_{T}[ V(T,P) ] = k·(1/P)
d_{P}[ V(T,P) ] = (-1)·k·( 1/P^{2} )